Ontology: How do ideas exist?

Question

There are several ways of looking at ideas.

There is a platonic way of looking at ideas which sees the ideas as kind eternal entities. Augustine puts these ideas in the mind of God. In either case they are eternal and immutable.

The proof is something like this: Was there any time when 1+1=2 was untrue? If there was no time when 1+1=2 is untrue, then it must have always been true that 1+1=2.

My question specifically is: Does this argument necessarily hold, and/or does someone have another idea of how ideas exist/what they are?

Answer 1

I'm having a little trouble connecting the dots between what you put at the top and your question.

What I see is :

(1) Definition of Forms for Plato / God's Ideas for Augustine as immutable and eternal entities.

Then

(2) If always 1 + 1 = 2, then 1+ 1. Ergo, this is eternal and immutable.

What I'm missing is the precise question you are asking as it relates to (1) and (2). As worded, I would say that (2) holds (being merely definitional -- something that is always is true eternally and immutably true) but does not necessarily force upon us the conclusion (1).

Specifically, I see two moves hidden between (2) and (1) that undermine the necessity. First, (1) posits eternal, immutable entities about substantive things in the world (Plato believes there's a form of horse, for instance) whereas (2) posits only a invariant proportion as eternal and immutable (which has no perfect physical instantiation).

Second, the argument in (2) is in Kant's vocabulary a priori and "synthetic" -- meaning that the manipulation is wholly contained in the definitions that 1 + 1 = 2 (synthesis of two incidents of the concept 1). Thus, it's not entirely clear that we are saying anything eternal or immutable so much as we are rearranging words. And that we can make this statement using only the reason we have (a priori).

Conversely, substantive forms/ideas are substantiated by objects in the world (either through the activity of the demiurge or the creator) as reflections on it. None of that is necessary to accept the continued veracity of 1 + 1 = 2.

To accept (2) is roughly to be committed to Mathematical Platonism.

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Separately, not everyone is committed to the eternal truth of 1 + 1 = 2. There are also other positions that posit that this is a function of our mental apparatus rather than reality. (See for instance the considerations at http://www.math.harvard.edu/~mazur/papers/plato4.pdf ).

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More generally, if your question is what other ways do people manage this than "ideas", then the answers that come to mind specifically (moving through history) are roughly in two categories:

1. Aristotle's essentialism. Aristotle thinks we get the real essences by abstracting essences from the objects we encounter. (differs mainly in that for Plato we recollect forms through anamnesis / for Augustine, we are helped by divine illumination ).

2. Conceptualisms - views where we have "concepts" in our mind but that these don't exist out there in things. One medieval version is called "Nominalism." This is generally the dominant view type today.

3. Kant's categories - sum of categories in the mind and features we encounter subsumed under these. (Hegel also has a type of category theory -- at least at points).

I could say more ... but I'm not sure which part is closest to the question you are asking.

Answer 2

There's different types of ideas:

Pasted in: Locke on Ideas David Banach

Ideas are the objects of thought and understanding. Whenever we think, perceive, or contemplate, we think about ideas.

All ideas come from Experience. Hence, all the materials of reason and knowledge arise from experience. None are innate. Experience may be of two different origins:

1. Sensation- These are ideas of external sensible objects conveyed to us by the senses: yellow, white, hot, cold.
2. Reflection- These are perceptions of the internal operations of our minds: thinking, doubting, willing.

Ideas from these sources may also be of two basic types: 1. Simple Ideas- Of one uniform appearance or conception in the mind; cannot be created or destroyed. 2. Complex ideas- Constructed by us in various ways using other simple ideas.

Simple ideas: These can be of four basic types:

1. Ideas from one sense: Light, noise, taste, smell, heat, solidity, texture. (secondary properties)
2. Ideas from more than one sense: space, extension, figure, rest, motion. (primary properties)
3. Ideas from reflection only: perception, willing.
4. Ideas from both sense and reflection: pleasure and pain, power, existence, unity.

Complex Ideas: These are constructed by us using three different methods:

1. Combination- putting various ideas together into one complex idea: a unicorn constructed from the ideas of horn and horse.
2. Relation- seeing the relation between ideas: equality.
3. Abstraction- separating one property from many particular ideas: all general, abstract ideas.

Complex ideas can also be of three different types of objects: A. Modes- these don't contain the supposition of independent subsistence. 1. Simple- combine same type of ideas: number (12). 2. Mixed- combine different types of ideas: beauty combines color and form. B. Substances- These represent distinct particular things. 1. Single- An individual taken to exist by itself: a man. 2. Collective- a group consisting of other individuals: an army or flock of sheep. C. Relations- These are relationships between other ideas, substances, or modes.